ΦΦΦΦAbstract – A new computationally efficient paradigm for the

design and analysis of switched reluctance machines is proposed.

At the heart of the rapid analysis and design methodology is the

reduced order computational method based on a flux tube model

which has been refined and extended. It is demonstrated how

the improved model enables consistent and accurate analysis

and design optimization. Instead of an analytical derivation, an

automatic generation of cubic splines is introduced to model the

magnetic flux. The flux linkage functions obtained from the

improved flux tube method indicate that the method offers good

accuracy compared to finite element based analysis, but with

significantly improved computational efficiency. The approach

is applicable to translating and rotating switched reluctance

machines of various topologies and therefore enables rapid

design search and optimization of novel topologies.

Index Terms -- nonlinear switched reluctance machine,

magnetic circuit analysis, flux tube modelling.

I. NOMENCLATURE

A : cross-sectional area

B : magnetic field density

H : magnetic field strength

l : flux tube cord length

R : total magnetic circuit reluctance

r : individual flux tube reluctance

N : number of conductor turns

t : tube, flux

I : electric current

V : magnetic field potential at a node

α : flux tube cross-sectional area error

ψ : flux linkage

λ : flux tube cord length error

π : magnetic field strength error

µ : magnetic permeability

ε : average error

ϕ : magnetic flux

‘ : estimated value

II. INTRODUCTION

WITCHED reluctance (SR) machines have attracted

substantial attention due to their simple and robust

construction. SR machines are as versatile, from

application point of view, as the well-established induction,

DC, and brushless permanent magnet electric machines. The

SR technology spans the following topologies: radial flux [1],

axial flux [2], transverse flux rotating machines [3], [4],

This work is supported by an EPSRC grant (EP/G03690x/1).

A. Stuikys and J. K. Sykulski are with the Department of Electronics

and Computer Science, University of Southampton, Southampton SO17

1BJ, United Kingdom (e-mail: A.Stuikys@soton.ac.uk / jks@soton.ac.uk).

translating (linear) machines [5], [6], and tubular translating

(linear) machines [7]. SR machine application areas are as

diverse as the more traditional electric machine technologies

mentioned earlier. For example, the radial and axial flux

machines have been used in many industrial drives, traction

motor and pumping applications [8]-[10]. The novel SR

linear machines have been used as magnetic propulsion and

levitation devices for railway systems in transportation [11].

The tubular linear SR machines were successfully tested in

medical applications as artificial heart pump actuators [12].

However, analysis and design of SR machines is a

complex task compounded by their non-linear behaviour.

Despite some effort [13] the analysis and design calculations

have not yet been developed into intuitive analytical tools

comparable to the methods available for the more established

types of machines such as induction or permanent magnet.

The main difficulty with the analysis and design of SR

machines is the magnetic nonlinearity caused by the heavily

saturated iron parts of the machine circuit. The non-saturating

SR machines, as used in some niche applications, are not

considered here.

Given the wide variety of topological arrangements of SR

machines, which is expected to grow in the future as the

demand for the new applications increases [14], it is vital to

establish computationally efficient analysis and design

methods. The aim is to make the design task more systematic

which in turn will open new application areas for the versatile

SR electric machine technology.

Reduced order computational methods, the most notable

example being the magnetic equivalent circuit (MEC)

approach, have been successfully employed in the past to

various types of electric machines [15]. The main advantage

of the MEC based models is that they are relatively accurate

given their computational efficiency. The finite element

analysis (FEA) is very useful for accurate analysis of the

established electric machine technologies, but it does not

offer the cause-and-effect insight when novel and unfamiliar

machine topologies are being considered [16]. Therefore,

bearing in mind the advantages of the MEC based analysis

methods, the design cycle is proposed as illustrated in Fig. 1.

First, a novel topology SR machine is identified and

considered for a certain application because it meets some

particular requirements imposed by the application, for

example: cost, volume and mass, mechanical, etc. Next, the

improved flux tube based method, which we propose in this

paper, is employed to construct the electromagnetic model of

the machine and is subsequently used in conjunction with a

design search and optimization algorithm, e.g. the genetic

algorithm (GA). Once a set of near optimal solutions (i.e. a

Pareto front) is obtained from the previous design cycle step,

Analysis and Design Framework for Nonlinear Switched Reluctance Machines

A. Stuikys, J. K. Sykulski

S

a few designs are identified for further optimization using an

order of magnitude more accurate analysis technique, such as

FEA. If FEA confirms that indeed these designs are near

optimal, the design cycle can conclude as the machine which

satisfies all the design constraints has been found. If,

however, the FEA proves otherwise, the knowledge and

insights gained from the flux tube modelling step are fed

back into the novel topology machine generation step and the

design cycle is repeated.

Fig. 1. The proposed SR machine design cycle using a reduced order

computational method of flux tubes.

III. FLUX TUBE MODELLING

MEC based modelling has been successfully used in the

past for rapid analysis of induction and permanent magnet

AC machines [17], as well as for SR machines [18]-[20]. In

this paper we propose an improved flux tube model for

analysis and design of SR machines, which offers

computational efficiency and simplicity compared to the

traditional analytical derivation of flux tubes as in [20].

First it is necessary to define what is meant by the term

flux-tube. Referring to Fig. 2: a flux-tube will have an

arbitrary length and an arbitrary cross-sectional area defining

a tube in which the magnetic flux is established due to the

unequal magnetic potentials Va and Vb.

Fig. 2. A system of flux tubes in parallel.

The trajectory of the tube, between the two nodes, can be

approximated by a combination of straight line and circular

arc segments. The material property, in which the flux-tube

exists, is defined by magnetic permeability and will, in

general, vary as a function of the magnetic potential along the

tube. If the material is air then the permeability of free space

is substituted, otherwise the magnetization curve of the

material must be used. To form a system of flux tubes in

three-dimensions (3D) the tubes are combined to fill the

entire 3D space.

Accurate magnetic reluctance estimation of the flux tubes

is important as this will determine the flux-linkage functions

of the SR machine defined as [16]

( )1.2

R

IN ⋅=ψ

In most general terms, and referring to Fig. 2, the flux tube

reluctance can be expressed as

( ) ( )( )2.

,,

1

0

∫ ⋅=

−=

l

baab dl

lAlba

VVR

µφ

The flux-linkage functions is all that is needed to describe

the SR machine performance, specifically the speed-torque

curve for a rotary machine or thrust force and corresponding

linear speed values for a translating machine. From these

characteristics the machine output power can readily be

found. The procedure will now be illustrated by an example.

A. A Flux Tube Modelling Example

The analysis of SR machines hinges on the ability to

accurately estimate the aligned and unaligned flux-linkage

functions as given in (1), which for the saturable machines

are always nonlinear for a range of excitation currents [21].

Again, this task is fairly easily accomplished with FEA based

methods; however, this approach may be computationally

inefficient if a near optimal design of novel and unfamiliar

topology machine is sought. Here we propose a method

based on the MEC approach. We will show how to obtain the

flux linkage functions for an SR machine by constructing

approximate flux tube distributions. It is important to note

that this approach is equally applicable to the modelling of

rotating and translating SR machines.

To illustrate the improved flux-tube based modelling a

translating (linear) switched reluctance machine (LSRM) is

considered. Figure 3 shows a typical LSRM geometry and the

resulting magnetic field distribution obtained from an

industry standard FEA. Due to the simple geometric (2D

planar) and spatial arrangement of the machine the magnetic

flux lines can be approximated using cubic-spline

representations of flux-tubes of the true flux paths.

Fig. 3. A double translator linear SR machine topology.

We start by inspecting the general flux function contour

and magnetic field density plot obtained from a standard FEA

analysis shown in Fig. 3. Next, due to symmetry, we reduce

the analysed magnetic circuit to that of symmetry segment

shown in Fig. 3. The proposed flux-tube analysis relies on the

ability to approximate the true flux tubes in the magnetic

circuit under study using smooth cubic splines.

Zooming into the symmetry segment of the LSRM shown

in Fig. 4, we recognize that in most electric machine

magnetic circuits of practical importance there will exist the

magnetic field equipotential regions.

Fig. 4. Subdivision of the symmetry segment into flux tube slices.

Utilizing this knowledge we can construct equipotential

slices across the flux paths of the magnetic circuit. Up to this

stage we were able to subdivide the circuit into four such

slices as shown in Fig. 4. However, an attempt to fit smooth

and continuous cubic spline approximations of the real flux

tubes between any two neighbouring slices using single set of

intermediate points would result in large interpolation errors

along the flux paths. This is because the actual flux tubes

have geometric discontinuities between the slices. Therefore,

it is necessary to subdivide the flux tubes along their lengths

even further. It is possible to do so by recognizing the very

important property of the flux tubes, that the flux tubes

normally enter magnetic material at a right angle to its

surface. Thus we are able to construct further slices, this time

along the magnetic material surfaces, termed ‘flux entry

points’ as in Fig. 4. Once the flux tube subdivision into slices

is complete, the cubic spline interpolation can be performed

as illustrated in Fig. 5.

Fig. 5. Cubic-spline approximations of the flux paths for the unaligned

translator position.

As is evident from the proceeding discussion and Fig. 4,

some prior experience and applying judgment will be helpful

when choosing the most representative and convenient

coordinate points for the cubic spline interpolation.

Using similar equipotential slice and flux entry point

placement techniques the aligned translator position flux-tube

approximations are obtained as in Fig. 6. Again, experience

and judgement are needed in order to accurately replicate the

true flux paths using cubic-spline approximations.

Fig. 6. Aligned translator position flux tubes obtained using cubic-splines.

Some simplifying assumptions are made when fitting the

splines in Fig. 6, in particular that there are no fringing or

leakage flux effects near the aligned rotor and stator poles as

would be expected in a practical machine. Moreover, the

energized stator pole flux tubes are approximated using

straight lines rather than cubic-splines. Again, this is an

approximation, but the resulting errors were found tolerable.

Finally, once the cubic spline approximations to the true

flux tube paths are complete, their individual reluctances can

be found from (2) as all the geometric information about the

tubes is known from the polynomial equation coefficients,

specifically the cross-sectional areas, cord lengths and

material properties. Therefore, flux linkage functions, as

given by (1), for these two translator cases are readily found.

B. Accuracy and Robustness of Flux Tube Modelling

In order to illustrate the accuracy and robustness of the

flux tubes method, from computation and numerical error

propagation point of view, analytical formulation is

employed. Figure 2 is used to describe what is meant by the

system of flux tubes.

1) Air Gap Reluctance: From Fig. 2 it is assumed that the

flux tube system is in the air gap or other non-magnetic

region of the SR machine. The flux tubes have been

subdivided into n slices along their lengths and cross-

sectional areas of each such slice averaged

( ) ( )3,,2,1,21 njAAA jjj K=÷+= +

Therefore, the individual reluctance of each of the m flux

tubes can be expressed as

( )4.1 0

∑= ⋅

==n

j j

j

tabA

lrR

µ

Now, because the system of flux tubes in Fig. 2 is

arranged in parallel, the total reluctance will be

( )5.1

...111

1

1 1 021

−

= =

∑ ∑

⋅=+++=

m

i

n

j j

j

tmttparallel A

l

rrrR µ

As argued in the previous section, the resulting flux tube

system of Fig. 5 approximates the FEA solution in Fig. 4

well, but is not exact. The flux tubes method considers

discretized systems rather than continuous. Thus it is

necessary to take two neighbouring cross-sectional areas of

each tube-slice and average them to produce a mean value for

that particular flux-tube slice as in (3). This averaging of

cross-sectional areas, however, will introduce some

numerical error. The error itself will vary from slice to slice,

and from tube to tube, and even from system to system.

Taking into account the numerical error thus created, (4) can

be expressed as follows

( )6....

'

0220

22

110

11

Ann

nln

A

l

A

lt

A

l

A

l

A

lr

εµ

ε

εµ

ε

εµ

ε

⋅⋅

⋅++

⋅⋅

⋅+

+⋅⋅

⋅=

⋅

It is assumed that each error term ε in (6) will be in the region

of, and unlikely to exceed, ±1.1 for the averaged cross-

sectional areas and cord lengths of each slice. If the number

of terms n in (6) is increased, the errors resulting from the

estimated cord lengths and cross-sectional areas of the tube

slices can be averaged, namely

( )7....'020

2

10

1

avA

avl

n

nt

A

l

A

l

A

lr

⋅

⋅×

⋅++

⋅+

⋅=

ε

ε

µµµ

For convenience, the averaged errors of the cross sectional

areas and cord lengths of each slice in (7) can be written as

( )8.; λεαε ⋅+=⋅⋅+=⋅ ⋅⋅ jjavljjjavAj lllAAA

It is now possible to show what impact the errors of the

estimated geometries will have on the reluctance value of the

whole system of tubes of Fig. 2. Rewriting (6) in terms of (8)

( )( )

( )( )

( )( )

( )( )

( )91

1

1 0

1

1...

1

1

1

1'

020

2

10

1

α

λ

µ

αµ

λ

αµ

λ

αµ

λ

+

+×

∑= ⋅

=

=+⋅⋅

+⋅++

+⋅⋅

+⋅+

++⋅⋅

+⋅=

n

j jA

jl

A

l

A

l

A

lr

n

n

t

and rewriting (5) in terms of (9)

( )( )

( )101

1

'

11

1 1 0 λ

α

µ +

+×

⋅=

−

= =

∑ ∑m

i

n

j j

j

parallel A

l

R

results in the total reluctance of the system of tube-slices in

series and combined in parallel to be

( )( )

( )11.1

1'

11

1 1 0 α

λ

µ +

+×

⋅=

−−

= =

∑ ∑m

i

n

j j

j

parallelA

lR

The result in (11) indicates that the estimated parallel

reluctance of the air gap tubes will scale linearly with the

quotient of the two errors. Thus it could be argued that if the

two error terms are both positive or both negative this will

tend to minimize the total error of the parallel reluctance. The

worst case scenario occurs if the two errors are of equal

magnitude but opposite sign, that is the cross-sectional areas

are underestimated whilst the cord lengths of the tubes are

overestimated, or vice versa. Even the worst case scenario is

considered to be tolerable provided the errors α and λ are not

larger than ±10% as stated earlier. Under such conditions the

total error can be no more than ±22%.

2) Iron Circuit Reluctance: In a similar way the reluctance

of the magnetically nonlinear iron circuit of the SR machine

can be estimated and effects of errors accounted for.

Consider Fig. 2 again, this time however with the magnetic

permeability no longer constant but varying according to the

magnetization curve of the material. Therefore (4) may be

rewritten, taking saturation into account, as

( )12.1

∑= ⋅

⋅==

⋅

⋅=

n

j jj

jj

t

abab

ababab

AB

lHr

AB

lHR

Assuming that the flux of each tube is of constant value the

magnetic field density occurring at each slice is

( )( )13

1''

α

φφ

+==

jj

jAA

B

and from (13) the following can be deduced

( )14.'0

'0

jj

jj

BBthenif

BBthenif

><

<>

α

α

In other words, if the error is positive the magnetic field

density will be underestimated compared to the true value

and vice versa. From the magnetization curve of Fig. 7 it

follows that the relationship between the erroneous magnetic

field density estimate and the resulting magnetic field

strength can be stated as

( )15.''

''

jjjj

jjjj

HHthenBBif

HHthenBBif

>>

<<

Fig. 7. A typical magnetization curve of a saturable iron circuit and the

resulting worst case errors in the non-saturated and saturated regions.

The resulting erroneous magnetic field strength for each of

the flux-tube slices along the lines of (8) can be expressed,

for convenience, as

( ) ( )16.1' ππ +=⋅+= jjjj HHHH

The estimated values in the denominators of (12) imply that

( )( )

( )171

1'

''' φ

α

αφφ=

+

+×=×=⋅

j

j

j

j

jjA

AA

AAB

which is trivial, however it does show that the estimated flux,

that is the denominator in (12), is not affected by the cross-

sectional area error α.

Equation (12) can now be expressed in terms of (16), also

remembering to include the tube slice cord length error term

derived earlier, as follows

( ) ( )

( ) ( )

( ) ( )

( ) ( ) ( )1811

1

11

...11

11'

22

22

11

11

λπ

λπ

λπ

λπ

+⋅+×

∑= ⋅

⋅=

=⋅

+⋅×+⋅+

++⋅

+⋅×+⋅+

+⋅

+⋅×+⋅=

n

j jA

jB

jl

jH

AB

lH

AB

lH

AB

lHr

nn

nn

t

and the parallel reluctance of the system of tubes in the iron

circuit is

( ) ( ) ( )19.11

'

11

1 1

λπ +⋅+⋅

⋅

⋅=

=

−−

= =

∑ ∑m

i

n

j jj

jj

parallel

AB

lH

R

Equation (19) indicates that the cross-sectional area

estimation error α has no influence on the final result of the

total reluctance of the iron circuit. However, a new error term

appears in (19) due to the estimation of magnetic field

strength from the non-linear iron magnetization curve.

Therefore, the total saturating iron reluctance will scale as a

product of the two errors. In contrast to the total air gap

reluctance, as in (11), the iron circuit reluctance value is

affected less by the equal magnitude but opposite signs of the

errors (that is when one is positive and the other is negative).

The worst case scenarios occur when both error terms are of

equal magnitude and either both positive, or both negative.

Attention is now turned towards the discussion of the

errors in (19) when the iron circuit is in the non-saturated and

when it is in the fully saturated regions of the magnetization

curve since steady-state SR machine operation takes place in

both of these regions. As can be seen from Fig. 7, the error

term for the magnetic field strength will be very small when

the flux-linkage values of the SR machine are estimated at

low phase excitation currents. The situation is very different

when flux-linkage values of the SR machine are estimated at

high phase excitation current levels where most of the iron

circuit is fully saturated. At this condition the π error term is

significantly larger, even if uncertainty associated with the

magnetic field density value is the same as in the non-

saturated region.

Due to the magnetic circuit design of the SR machine used

here for illustrative purposes, the air gap and iron circuit

components are arranged magnetically to be in series. Thus

for the both the aligned and unaligned flux-linkage function

estimations, the reluctances given by (11) and (19) will be

additive, while the error terms for the unaligned flux-linkage

curve will be order of magnitude smaller compared to the

error terms of the aligned flux-linkage curve. This effect is

due to the point made above, but to repeat: the saturated

reluctance error of the aligned SR machine circuit will be

exacerbated due to error terms in (19), whereas in (11) the

error will be negligible as the air region’s length is small as in

Fig. 6. On the other hand, the reluctance error of the

unaligned SR machine circuit will be made worse due to

increased error terms in (11) as the air-gap region’s length is

large, whereas in (19) the error will be relatively much

smaller because of the non-saturated state of the iron as in

Fig. 5.

The preceding error analysis of the flux tube approach,

and in particular expressions (11) and (19), can be directly

compared to the ‘tubes-and-slices’ (TAS) method used to

analyse electric and magnetic fields in linear media [22]. The

analytical TAS derivation, in addition to using the tubes,

makes use of the construction of a system of slices along the

lines of Fig. 2, leading to the creation of dual bounds. The

tubes result in a lower bound of the permeance, whereas the

slices in an upper bound. There is similarity to the calculation

of a resistance or capacitance, with the analogue of the

permeability, µ , being the conductivity, σ, or permittivity, ε,

respectively. The bounds are guaranteed and thus the true

answer always lies between the two values. Taking an

average often results in a good numerical approximation.

It may be possible to adapt the flux tube approach if the

resulting error of the system of tubes is to be minimized. A

possible strategy is to compare the flux-linkage function

based on a particular flux-tube system with a FEA solution

and use the numerical error found to correct the subsequently

generated systems of flux tubes. Such a strategy would be

likely to be most effective when a large number of flux tube

systems is being generated, as in GA based optimization.

IV. FLUX TUBE MODEL RESULTS

The proposed flux tube model has been applied to a wide

range of SR machine geometries to test if the new method

consistently and accurately predicts the performance. To

accomplish this, six machine design parameters were selected

and varied in order to generate distinct machine geometries.

Referring to Fig. 3, the following variables were designated:

translator back iron thickness, translator pole height, stator

and translator pole pitch, the pole width, number of turns per

coil, machine stack thickness.

Figure 8 compares the aligned and unaligned flux-linkage

functions, assuming flat-topped current profile as in [16],

obtained with the improved flux tube method and using

commercial FEA. The unaligned flux-linkage functions from

both methods compare very well and even such effects as the

onset of saturation at higher phase currents, 150A and

slightly above, are also captured by the flux tube model.

Clearly the unaligned flux-linkage function is linear up to the

peak flat-topped current, 150A in this case. Therefore the

saturation effects and, more importantly, the numerical

discrepancy from the FEA result will not affect the machine

performance prediction in any noticeable way.

Fig. 8. Flux-linkage functions using the flux-tube method and FEA.

The aligned flux-linkage functions obtained from the two

methods show some numerical discrepancies, although they

are not large. Assuming that the aligned flux-linkage function

obtained using FEA software is correct, the flux tube method

underestimates the value by 7% at the peak current of 150A.

The error is reassuringly low, bearing in mind that the flux

tube model of Fig. 6 used only 12 flux-tube slices, which is a

coarse subdivision compared to the fine mesh used in FEA.

Even more importantly, the aligned flux-linkage function

obtained by the flux tube method preserves the ‘true’ shape

of the aligned flux-linkage function as obtained with FEA.

This fact, already observed and reported in literature [21] and

evident from Fig. 9, has far reaching implications and greater

importance – when determining instantaneous torque and

phase current waveforms – than the exact numerical answer

at only saturated or only unsaturated machine states. Finally –

as expected – the accuracy of the approximate prediction

becomes worse in the heavily saturated region of the aligned

position, but this is of no practical consequence as the

operating current is above the peak value; this part of the

curve has been included for completeness, but should be

disregarded in the context of the design process.

Fig. 9. Comparison of current and instantaneous torque waveforms

obtained with the flux tube method and FEA.

Consequently, from a visual comparison of the functions

in Fig. 8, it is evident that the numerical discrepancies are not

as significant compared to the similarity of shapes. Drawing

the knowledge gained from the above presented analytical

derivation of the flux tube method, it is now clear that the

answer given by (19) is more sensitive to the estimated

magnetic field strength values in the saturated region than to

the non-saturated region of Fig. 7. In this particular case the

total circuit reluctance is overestimated, which is

conservative, giving the lower aligned flux-linkage function

as in Fig. 8.

The instantaneous torque and phase current waveform

comparison is important when assessing the improved flux

tube method accuracy. Similarly, it is very useful to compare

the speed-torque characteristics of the translating SR

machine. The machine geometry is first converted from the

translating machine domain to the rotating machine domain,

as described in [16], to facilitate ease of comparison. Fig. 10

compares speed-torque characteristic envelopes obtained by

the flux-tube method and FEA.

Fig. 10. Speed-torque envelopes of the flux tube method and FEA.

Again, from the visual comparison of superimposed

envelopes, it is evident that the flux tube method accurately

and consistently predicts the average torque values,

consistent with the FEA results, over a wide speed range. In a

similar way the speed-power envelopes of the SR machine

are compared in Fig. 11.

Fig. 11. Speed-power envelopes of the flux tube method and FEA.

As argued in this paper, the method of the flux tubes has

been demonstrated to possess the necessary consistency and

accuracy, while being general in scope of applications. It can

be applied to rotating SR machines and to a wide range of SR

machine topologies more generally.

A possible enhancement of the method might include a

direct incorporation of the dual bounds concepts by adding a

second calculation based on slices, as in the original tubes-

and-slices approach. However, this needs to be considered

with care as the additional effort and associated extended

computing times may not necessarily be justified since the

application of flux tubes alone appears to provide sufficient

accuracy while preserving computational efficiency necessary

for the rapid design purposes of Fig. 1.

Finally, it should be noted that the purpose of this work is

to improve the practicality of the design process, normally

relying on finite element modelling, by supplementing it with

a much more computationally efficient methodology

exploiting semi-analytical flux-tube field description. The

appropriateness of the finite element approach has been

proven before, including experimental verification. In this

work we focus on improving the speed of numerical analysis

while preserving the original level of accuracy.

V. CONCLUSIONS

The paper has introduced a new analysis and design

paradigm in application to SR machines. It is believed that

the proposed design cycle will enable systematic and

computationally efficient effort to be expended when novel

and unfamiliar topology SR machines are considered for new

applications. To speed up the design search and optimization

task an improved flux tube modelling has been proposed. The

improved method enables rapid analysis and design of

electromechanical devices, in particular efficient estimation

of flux-linkage functions used to describe the operation of SR

machines. It has been demonstrated that the flux tube method

can relatively accurately and consistently predict these flux

linkage functions, including such effects as magnetic

saturation and flux leakage. It is concluded that the

inaccuracies generated by the flux tube method are small and

do not introduce unacceptable errors in the values of

predicted currents and torques, both instantaneous and

average. Therefore the method is suitable for rapid initial

design search and optimization of SR machines of various

topologies.

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VII. BIOGRAPHIES

Aleksas Stuikys received the B.Sc. degree in Mechanical Engineering from

Oxford Brookes University, Oxford, UK, in year 2009. He received the

M.Sc. degree in Advanced Engineering Design in year 2011 from the same

institution. After a number of years working in automotive industry as an

engineer he returned to academia to pursue the doctoral degree at the

Institute for Complex Systems Simulation, School of Electronics and

Computer Science, University of Southampton, Southampton, UK. His

research interests span the fields of propulsion systems, including electric

traction motors; their modelling, simulation and design for the electric and

hybrid vehicles and for the sustainable transport in general. This research

also includes the modelling, design and control aspects of switched

reluctance machines and traction systems.

Jan Sykulski is Professor of Applied Electromagnetics at the University of

Southampton, UK. His personal research is in development of fundamental

methods of computational electromagnetics, power applications of high

temperature superconductivity, simulation of coupled field systems and

design and optimisation of electromechanical devices. He has published

over 370 scientific papers and co-authored four books. He is founding

Secretary of International Compumag Society, Visiting Professor at

universities in Canada, France, Italy, Poland and China, Editor of IEEE

Transactions on Magnetics, Editor-in-chief of COMPEL (Emerald) and

member of International Steering Committees of several international

conferences. He is Fellow of IEEE (USA), Fellow of the Institution of

Engineering and Technology (IET), Fellow of the Institute of Physics (IoP),

Fellow of the British Computer Society (BCS), Doctor Honoris Causa of

Universite d’Artois, France, and has an honorary title of Professor awarded

by the President of Poland. http://www.ecs.soton.ac.uk/info/people/jks .